We argue that the best estimate of the effects of campaign contact and advertising is zero

From The Minimal Persuasive Effects of Campaign Contact in General Elections: Evidence from 49 Field Experiments by Joshua Kalla and David E. Broockman. I am not surprised by the finding but I also find it hard to reconcile with the conviction of campaigns that they need to advertise.

Significant theories of democratic accountability hinge on how political campaigns affect Americans' candidate choices. We argue that the best estimate of the effects of campaign contact and advertising on Americans' candidates choices in general elections is zero. First, a systematic meta-analysis of 40 field experiments estimates an average effect of zero in general elections. Second, we present nine original field experiments that increase the statistical evidence in the literature about the persuasive effects of personal contact 10-fold. These experiments' average effect is also zero. In both existing and our original experiments, persuasive effects only appear to emerge in two rare circumstances. First, when candidates take unusually unpopular positions and campaigns invest unusually heavily in identifying persuadable voters. Second, when campaigns contact voters long before election day and measure effects immediately---although this early persuasion decays. These findings contribute to ongoing debates about how political elites influence citizens' judgments.

The research suggests that such advertising makes no difference, but the practitioners are convinced that it does. Where's the truth?

Of course we have some additional real-world data from the last campaign. Clinton spent some hundreds of millions more than Trump on advertising, but to no end. Disentangling money spent on advertising, the press's support for Trump in the primary and opposition during the election, and Trump's own Sevengali-like ability to create free press coverage and dominate news-cycles, of course makes analysis quite difficult to determine relative causes, effects, and effect-sizes.

The effect-size of advertising on campaign outcomes remains a mystery to me. I suspect it does make a difference under very particular circumstances but that we, in general, do not understand what those particular circumstances might be.